ICF image restoration using Iterative Regularization methods

Inertial confinement fusion (ICF) is an approach to fusion that relies on the inertia of the fuel mass to provide confinement. A capsule generally is a spherical shell filled with low-density gas (~1.0 mg/cm³). The shell is composed of an outer region, which forms the ablator, and an inner region of frozen or liquid deuterium-tritium (DT), which forms the main fuel. Energy from a driver is delivered rapidly to the ablator, which heats up and expands. As the ablator expands outward, the rest of the shell is forced inward to conserve momentum. X-ray imaging diagnostics revealed correlated signatures of azimuthal implosion asymmetry. This low-mode asymmetry degrades hot-spot conditions at peak convergence that limits implosion performance. One biggest challenge is to retrieve useful information and insight from sparse and noisy ICF images. In this project, a linear inverse problem of the form b=Ax+n is investigated, where b represents the vector of the blurred image and A represents the blurring matrix. Given A and b, the aim is to compute an approximation of the unknown x. Iterative regularization is a good alternative to direct regularization method. In this project two different iterative regularization approaches are explored. The hybrid flsqr and heuristic total variation methods have demonstrated a good mathematical basis for image restoration of ICF images. An efficient regularized solution is produced when the iteration is terminated at minimum error. Out of all the methods mage restoration algorithms, only these two are compared because of their outstanding performance on ICF images. Algorithm validation use synthetic images with noises, and then compared with a synthetic image which do not have any noise. To verify the image quality, SSIM scores are computed. Initial analysis of experimental data using the validated algorithms are also given.